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Extra info for Experimental Research in Evolutionary Computation
The Observed Signiﬁcance Level The frequency relation between a rejection of the null hypothesis H and values of the diﬀerence in means, δ, is important for the interpretation of the rejection. 8) αd (δ) = α(d, δ) = Pr(Y1 − Y2 ≥ d|δ). Hence, αd (δ) is the area under the normal curve to the right of the observed d, as illustrated in Fig. 4. If we set δ0 = 0, then αd (δ0 ) is the frequency of an error of the ﬁrst kind. If αd (δ0 ) ≤ “the preset signiﬁcance level of the test RU ,” then RU rejects H with d.
As common or antithetic seeds can be used, the optimization practitioner has much more control over the noise in the experiments and can control the source of variability (Kleijnen 1997). The diﬀerent optimization runs for one speciﬁc factor combination can be performed under exactly the same conditions—at least in principle: Even under exactly the same conditions diﬀerent hardware can produce unexpected results. To compare diﬀerent run conﬁgurations under similar conditions variance-reduction techniques (VRT) such as common random numbers (CRN) and antithetic variates can be applied (Law & Kelton 2000).
6 Popper and the New Experimentalists In a similar manner as Gigerenzer (2003) presents his tools to theories approach, Mayo suspects that Popper’s falsiﬁcation theory is well accepted by many scientists since it reﬂects the standard hypothesis testing principles of their daily practice. To clarify the diﬀerence between Mayo’s NPT∗ approach and Popperian testing, the reader may consider the following quotation: Mere supporting instances are as a rule too cheap to be worth having: they can always be had for the asking; thus they cannot carry any weight; and any support capable of carrying weight can only rest upon ingenious tests, undertaken with the aim of refuting our hypothesis, if it can be refuted (Popper 1983).